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Extensions of the duality between minimal surfaces and maximal surfaces. (English) Zbl 1211.53010

Author’s abstract: As a generalization of the classical duality between minimal graphs in \(E^{3}\) and maximal graphs in \(L^{3}\), we construct the duality between graphs of constant mean curvature \(H\) in Bianchi-Cartan-Vranceanu space \(E^{3} (\kappa , \tau )\) and spacelike graphs of constant mean curvature \(\tau \) in Lorentzian Bianchi-Cartan-Vranceanu space \(L^{3}(\kappa , H)\).

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
35J60 Nonlinear elliptic equations
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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